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Math 2200 Homework 3 Key Problem 1 Compute the radius and interval of convergence for
 

Summary: Math 2200 Homework 3 Key
Problem 1 Compute the radius and interval of convergence for
f(x) =

n=0
(-2x)n
.
Solution: use the ratio test:
Lim
n
(-2x)n+1
(-2x)n
= |2x| < 1
So |x| < 1
2
and the radius of convergence is r = 1
2
. Plugging in 1
2
for x to check the endpoints we get

  

Source: Ashlock, Dan - Department of Mathematics and Statistics, University of Guelph

 

Collections: Mathematics